Synchronization of slow-fast systems

We describe different patterns of synchronization of two systems, each possessing oscillations on two very different time scales. Synchronization of slow and fast oscillations are characterized separately, leading to a possibility to observe partially synchronized states where, e. g., the slow motions are synchronous while the fast are desynchronized. As a first example we study two diffusively coupled Hindmarsh-Rose oscillators in the regime of regular or chaotic bursting and describe different synchronous states like phase synchronization of slow variables, burst and spike synchronization of fast variables, and complete synchronization. Next, we study two coupled four-dimensional model systems with chaotic slow dynamics and find phase synchronization of slow motion, complete and partially complete synchrony.